JP4608430B2 - Scanning optical system, scanning optical apparatus using the same, and image forming system - Google Patents

Description

  The present invention relates to a scanning optical system, a scanning optical apparatus using the same, and an image forming system. For example, the present invention relates to a scanning optical system that performs scanning by obliquely injecting a plurality of light beams into one optical deflector from the sub-scanning direction, a scanning optical device using the same, and an image forming system.

Conventionally, in a scanning optical system used in an image forming system such as a tandem color printer, for example, a plurality of light beams are incident on an optical deflector, deflected by the optical deflector, and incident on a first lens optical system. A plurality of light beams emitted from the lens optical system are guided to different second lens optical systems, and spot light is generated on different imaging surfaces by the imaging optical system constituted by the first lens optical system and the second lens optical system. A scanning optical system that forms an image and performs constant-speed scanning is used.
Then, for example, a single optical deflector is required, and the cost is reduced, so that a plurality of light beams incident on the optical deflector are incident on a plane perpendicular to the rotation axis of the optical deflector from an oblique direction. In some cases, a method of oblique incidence in which the light is obliquely incident from the sub-scanning direction is employed.
In the oblique incidence type scanning optical system, scanning line bending occurs during light deflection, and the linearized beam near the optical deflector enters the scanning lens in a rotated state. However, there is a problem of spot diameter degradation on the photoreceptor, and various scanning optical system proposals have been proposed to solve them.
For example, Patent Document 1 discloses a scanning optical apparatus and a laser beam printer apparatus (image forming system) that perform two-beam scanning by an oblique incidence method, using a cylindrical lens as a first lens optical system, and a second lens optical system. As a scanning optical system, a two-stage toric lens having a curved bus or a two-stage toric lens whose lens surface in the sub-scanning direction is inclined with respect to the optical axis is described. This toric lens is a rotationally asymmetric lens composed of spherical surfaces having different curvatures in the main scanning section and the sub-scanning section.
Further, in Patent Document 2, two lenses are arranged on the optical path of light that is obliquely incident and deflected, and the tilt amount of the sub-scanning cross-sectional shape changes in the main scanning direction on at least two of them. A scanning imaging optical system (scanning optical system) including a special tilt surface, an optical scanning device (scanning optical device), and an image forming device (image forming system) are described.
In Patent Document 3, a scanning optical system includes a front lens group (first lens optical system) and a rear lens group (second lens optical system), and the front lens group includes a rotationally symmetric aspheric lens. The rear lens group has a rotationally asymmetric aspheric surface represented by a polynomial of Y and Z, where Y is the main scanning direction coordinate from the optical axis and Z is the sub-scanning direction coordinate, and the rear lens The group is described in an eccentric arrangement with respect to four obliquely incident beams.
JP-A-10-73778 (FIGS. 1, 2, 5, and 11) Japanese Patent No. 3453737 (FIGS. 1 and 2) Japanese Patent Laid-Open No. 2003-5113 (FIGS. 2, 3, and 14)

The conventional scanning optical system as described above, and the scanning optical apparatus and image forming system using the same have the following problems.
In the technique described in Patent Document 1, after being deflected by an optical deflector, light is condensed in the sub-scanning direction by a cylindrical lens. However, since the tilt angle of the beam due to oblique incidence is not corrected, the scanning locus is on the toric lens. In order to correct a large curvature, it is necessary to eccentrically arrange a toric lens having a curved generating line in the same manner as the scanning locus. Therefore, the effective lens surface of the toric lens in the sub scanning direction becomes large. Further, since the curved surface is asymmetric in the sub-scanning direction, if the shape of the lens in the main scanning direction is asymmetric with respect to the central optical axis, two types of upper and lower toric lenses are required, leading to high costs. If the shape in the main scanning direction is symmetric with respect to the central optical axis, only one type is required, but this is not preferable because the degree of freedom in design is reduced.
In the techniques described in Patent Documents 2 and 3, there is a similar problem, and “special tilt surface” or “aspherical surface including Y and Z polynomials” is applied to the scanned side lens of the tandem optical system. As long as the shape of the lens in the main scanning direction is not symmetric with respect to the central optical axis, two types of toric lenses are required, resulting in a cost increase.

  The present invention has been made in view of the above problems, and has a simple and inexpensive configuration when performing a plurality of beam scans on the optical deflector and the first lens optical system by a so-called oblique incidence method. It is an object of the present invention to provide a scanning optical system that can perform scanning, a scanning optical device using the same, and an image forming system.

In order to solve the above problems, the scanning optical system of the present invention deflects a plurality of light beams from a light source by entering the light deflector from an oblique direction on a plane orthogonal to the rotation axis of the light deflector, The plurality of light beams are incident on the first lens optical system obliquely in the sub-scanning direction, and the plurality of light beams emitted from the first lens optical system are respectively incident on the second lens optical systems having different arrangement positions. A scanning optical system that performs image scanning on different imaging planes and performs a plurality of beam scans, wherein the first lens optical system has at least two free-form surfaces, and the first lens optical system With respect to the positional relationship with the second lens optical system, the light beam emitted from the first lens optical system passes through the center reference position of the lens surface on the entrance surface and the exit surface of the plurality of second lens optical systems, and is subjected to main scanning. Straddling the lens center line extending in the direction And positional relationship to draw査軌traces, the second lens optics sub-scanning direction cross-sectional shape is assumed to be symmetrical configuration with respect to the lens optical axis.
According to the present invention, since various aberrations are corrected mainly by the two free-form surfaces in the first lens optical system, even if the second lens optical system having a symmetrical shape in the sub-scanning direction is used, It is possible to sufficiently correct scanning line bending due to light deflection, deterioration of a spot diameter due to rotation of a linear beam, and the like. Therefore, even if the shape of the main scanning side of the second lens optical system is asymmetrical, a common lens is sufficient for the upper and lower sides. In addition, since the position of the light beam on the incident / exit surface of the second lens optical system can be brought close to the center of the lens, the effective surface of the lens optical system can be reduced, and productivity is improved.

  In this specification, the main scanning direction and the sub-scanning direction are used in a broad sense, that is, not only in the direction on the surface to be scanned but also in the case of referring to two directions of a cross section orthogonal to the optical axis. That is, the direction corresponding to the main scanning direction and the sub-scanning direction on the image plane when traveling along the optical path and reaching the image plane is referred to as the main scanning direction and the sub-scanning direction, respectively, at any position on the optical path.

  According to the scanning optical system, the scanning optical apparatus and the image forming system using the scanning optical system of the present invention, the first lens optical system has two free-form surfaces, so that the scanning locus of the light beam on each second lens optical system. Since the scanning trajectory straddling the center axis of the second lens optical system is drawn by appropriately setting the position and the amount of curvature, the effective range of each second lens optical system is narrowed while maintaining good optical performance. And productivity can be improved. In addition, since the shape of the second lens optical system on the sub-scanning side can be made symmetric, even if the shape of the lens optical system in the main scanning direction is asymmetric, only one lens is required, and the degree of freedom in design is improved. To do.

  Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings. In all the drawings, even if the embodiments are different, the same or corresponding members are denoted by the same reference numerals, and common description is omitted.

A scanning optical system according to an embodiment of the present invention will be described together with a scanning optical device and an image forming system using the scanning optical system.
FIG. 1 is a cross-sectional view along a sheet passing direction schematically showing a schematic configuration of a scanning optical apparatus and an image forming system according to an embodiment of the present invention. FIG. 2 is a plan view schematically showing a schematic configuration of the light source unit of the scanning optical system according to the embodiment of the present invention. 3A and 3B are schematic optical path diagrams in the main scanning direction and the sub-scanning direction for explaining the configuration of the scanning optical system according to the embodiment of the present invention. FIG. 4 is a ray diagram in the main scanning direction of the scanning optical system according to the embodiment of the present invention.
In the following, for the convenience of relative direction reference, there may be used a ξηζ right-handed orthogonal coordinate system which is a common fixed coordinate system described in the drawings. In this coordinate system, the positive direction of the ζ axis is vertically upward, and the ξη plane coincides with the horizontal plane. Here, the negative direction of the η axis coincides with the transfer paper conveyance direction of the image forming system. The main scanning direction of the optical scanning device 1 is along the ξ-axis direction and the sub-scanning direction is along the η-axis direction on the surface to be scanned.

  As shown in FIGS. 1 and 2, the optical scanning device 1 of the present embodiment deflects light from four light sources with one optical deflector and performs beam scanning with four light beams. Hereinafter, an example in which the image forming system 200 is configured in combination with the image forming apparatus 50 will be described. The image forming system 200 can be suitably used for, for example, a laser printer or a digital copying machine that forms a four-color full-color image.

  As shown in FIGS. 1 to 3, the schematic configuration of the optical scanning device 1 includes beam light sources 5A, 5B, 5C, 5D, four cylindrical lenses 6, a polygon mirror 8, a polygon motor 9, two first lenses 11, It consists of two folding mirrors 20, 21, four second lenses 12, two folding mirrors 22, 23, four protective glasses 13, and a housing 15 that holds them fixedly in a fixed positional relationship.

The beam light source 5A generates laser light 30A having an appropriate diameter in the main scanning direction and the sub-scanning direction, with appropriate convergence, and is a semiconductor laser (hereinafter referred to as LD) 2A that emits divergent light of a certain wavelength. Collimating lens 3 for converging diverging light from LD 2A to form a beam having a certain convergence property, collimating lens so that an appropriate imaging spot diameter can be formed in the main scanning direction and sub-scanning direction on the image plane. 3 includes an aperture 4 that shapes the beam shape of the beam emitted from the beam 3.
The convergence degree of the laser light 30A may be any of convergent light, parallel light, and divergent light depending on the design conditions of the scanning optical system, but in this embodiment, the convergent light is used, and there is no subsequent optical system. Assuming that the distance from the position of the first surface 6a of the cylindrical lens 6 to the convergence position is 44 8 . 1 mm.
As the aperture 4, a member in which an opening having an appropriate size such as an elliptical shape, a rectangular shape, or an oval shape is formed on the light shielding plate can be used. The size of the aperture is appropriately set according to the spot size required on the image plane and the optical characteristics of the scanning optical system.

The beam light sources 5B, 5C, and 5D generate laser beams 30B, 30C, and 30D similar to the laser beam 30A, respectively, and include LDs 2B, 2C, and 2D, respectively, instead of the LD 2A of the beam light source 5A.
In the following, for the sake of simplicity, the members having the suffixes A, B, C, and D attached to the reference may be collectively referred to as A to D. For example, beam light sources 5A to 5D mean beam light sources 5A, 5B, 5C, and 5D.

Each cylindrical lens 6 condenses the laser beams 30A to 30D emitted from the beam light sources 5A to 5D only in the sub-scanning direction, and on the two deflection surfaces 8a and 8b of the polygon mirror 8, respectively. This is an optical element that forms an image in a line extending in the direction.
In this embodiment, as shown in FIGS. 1 and 2, the polygon mirror 8 is formed in a fixed direction by a polygon motor 9 having six deflection surfaces parallel to the ζ-axis direction that form a regular hexagon and a rotation axis along the ζ-axis. A rotating polygon mirror that rotates at a constant speed. Therefore, light incident from a plane parallel to the ξη plane can be deflected in a certain direction within a plane parallel to the ξη plane.

In the present embodiment, as shown in FIG. 2, the beam light sources 5A and 5B and the cylindrical lens 6 and the beam light sources 5C and 5D and the cylindrical lens 6 are respectively the rotation axes of the polygon motor 9 when viewed from the positive direction of the ζ axis. Are arranged on the plane side symmetrical with respect to the negative side of the η axis and the positive side of the η axis with respect to the plane parallel to the ζξ plane including the rotation axis of the polygon motor 9. Yes.
Then, the laser beams 30A and 30B emitted from one cylindrical lens 6 are incident on the deflection surface 8a of the polygon mirror 8, and the laser beams 30C and 30D emitted from the other cylindrical lens 6 are incident on the deflection surface 8b. Placed in.
Further, the laser beams 30A and 30D are incident from the ζ axis positive direction side, and the laser beams 30B and 30C are incident from the ζ axis negative direction side at an inclination angle φ ₁ (see FIG. 3B) with respect to the ξη plane. Is done. That is, the light beam is obliquely incident at an inclination angle φ ₁ in the sub-scanning direction cross section including the optical axis.

Disposed on the optical path between each cylindrical lens 6 and the beam source 5A-D, the beam splitter 7, 7-beam light source 5A, 5B and, beam light source 5C, and 5D, small values of the inclination angle phi ₁ Are optical path combining means for arranging them at positions that do not overlap in the ζ-axis direction so that they can be arranged without interfering with each other.
The beam splitter 7 has a beam splitter characteristic that transmits the laser beams 30B and 30C and reflects the laser beams 30A and 30D.
As the beam splitter 7, for example, a half mirror or a beam splitter prism can be adopted. Further, when the polarization directions of the laser beams to be combined are set in directions orthogonal to each other, a polarization beam splitter may be employed.

The first lens 11 and the second lens 12 constitute a scanning lens system 10, and the laser beams 30 </ b> A to 30 </ b> D deflected by the polygon mirror 8 are scanned on the scanned surface 14 (see FIG. 3) in the main scanning direction and the sub scanning direction. And fθ correction characteristics for forming an image in a spot shape having a substantially constant spot diameter and scanning at a constant speed in the main scanning direction according to the rotation of the polygon mirror 8 at a constant angular speed.
Further, the scanning lens system 10 has a conjugate relationship between the deflection surface 8b and each scanned surface 14 in the cross section in the sub-scanning direction. For this reason, surface tilt correction of the deflection surface 8b is performed.

  Since the optical paths of the laser beams 30A and 30B are easily understood from the symmetry of the arrangement, the description thereof will be omitted. Hereinafter, the folding of the optical path is developed to illustrate the beam splitter 7 and the folding mirrors 20, 21, 22, and 23. Description will be made along the optical paths of the laser beams 30C and 30D with reference to FIGS. 3A and 3B as appropriate.

In the present embodiment, the first lens 11 has an absolute value of position coordinates in the sub-scanning direction with respect to the center reference position as X = √ (x ² ), and an absolute value of position coordinates in the main scanning direction as Y = √ (y ² ), it is a free-form surface composed of a rotationally asymmetric aspheric surface expressed by a mathematical formula including a polynomial of X and Y, and a single lens composed of a first surface 11a and a second surface 11b. The center reference position is coincident with the optical axis passing through the image height 0 that is the scanning center in the main scanning direction and parallel to the η axis.
For example, a free-form surface expression represented by the following expression (1) can be adopted.

Here, the sum symbols m and n are integers of 0 or more, and A _mn represents an aspheric coefficient.
The xyz coordinate system representing the lens surface has an origin at the center reference position of the lens surface. In the first lens 11, the axial main axis of the light beam incident on the polygon mirror 8 at φ ₁ = 0 °. A z-axis is provided on an optical reference axis 41a (see FIG. 3B) that represents the direction in which the light beam travels. In FIG. 2, the ξ-axis negative direction is the y-axis positive direction and the ζ-axis positive direction is the x-axis positive direction. Is an orthogonal coordinate system.
3A and 3B are schematic diagrams, the cross-sectional shapes of the first lens 11 and the second lens 12 are drawn in a shape unrelated to the actual shape.
A specific cross-sectional shape of the first lens 11 in the main scanning direction is shown in FIG.

As shown in FIG. 3 (b), the laser beam 30D is the inclination angle phi ₁ in the illustrated obliquely downward deviation portions from the optical axis in the sub-scanning direction of the first lens 11 (zeta axial negative direction in FIG. 1) The light is transmitted and condensed while being refracted toward the optical axis. Similarly, the laser beam 30C is not particularly shown, passes obliquely upwardly deviation portions on the opposite side in the sub-scanning direction at a tilt angle each phi _1, is refracted toward the optical axis while being converged. Therefore, in the present embodiment, the cross-sectional shapes of the first surface 11a and the second surface 11b in the sub-scanning direction are plane-symmetric with respect to a plane that passes through the lens optical axis and extends in the main scanning direction.
However, since the first surface 11a and the second surface 11b are polynomials of X and Y, the degree of freedom of the shape of the curved surface is improved. For example, the laser beams 30C and 30D are inclined differently in the sub-scanning direction with respect to the optical axis. When incident at an angle, the cross-sectional shape may be asymmetric in the main scanning and sub-scanning directions. In addition, when the term of the product of X and Y is included, a lens surface having a correlation between X and Y can be created. A refractive power can be imparted.

  In addition, the sub-scanning cross-sectional shape at each position in the main scanning direction has an image height so that the amount of curvature of the scanning locus on the first surface 12a that is the incident surface of the second lens 12 is reduced at each light transmission position. The setting changes accordingly. This is easily realized by making the first surface 11a and the second surface 11b into free-form surfaces represented by mathematical expressions including X and Y polynomials.

The second lens 12 is a long single lens that condenses the laser light 30C emitted from the first lens 11 on the scanned surface 14 side, and both the first surface 12a and the second surface 12b are in the sub-scanning direction. The cross-sectional shape is symmetric with respect to the optical axis of the lens, and it consists of a spherical surface or a spherical surface whose curvature radius changes continuously in the main scanning direction, and an aspherical surface is formed in the main scanning direction. Consists of including aspheric surfaces.
For example, an aspherical expression represented by the following expression (2) can be adopted.

Here, x and y are position coordinates in the sub-scanning direction and the main scanning direction with respect to the center reference position of the lens surface, and X = √ (x ² ) and Y = √ (y ² ). The sum symbol m is an integer of 0 or more, and A _m and B _m represent aspherical coefficients. Further, CUY and CUX are reciprocals of the paraxial curvature radius of the cross section in the sub-scanning direction, respectively.
The xyz coordinate system representing the lens surface has an origin at the center reference position of the lens surface. In the second lens 12, the center reference position of the second surface 11b that is the exit surface of the first lens 11 is used. The coordinate system is set as a coordinate system that moves by d _{5 in the} positive z-axis direction, moves by H in the negative x-axis direction, and rotates by an angle φ ₂ from the positive x-axis direction to the positive z-axis direction.
A specific cross-sectional shape of the second lens 12 in the main scanning direction is shown in FIG.

As shown in FIG. 1, the folding mirror 20 deflects the laser light 30C transmitted through the first lens 11 and obliquely emitted toward the ζ axis positive direction side toward the ζ axis negative direction and the η axis negative direction side, An optical path to be incident on the second lens 12 whose optical axis is inclined at a predetermined angle in the ηζ plane is formed.
The folding mirror 22 deflects the laser light 30C transmitted through the second lens 12 in the positive z-axis direction.
The folding mirror 21 deflects the laser beam 30D transmitted through the first lens 11 and obliquely emitted toward the negative ζ-axis direction in the negative ζ-axis direction and the negative η-axis direction so as to have a predetermined angle within the ηζ plane. An optical path to be incident on another second lens 12 having an inclined optical axis is formed.
The folding mirror 23 deflects the laser light 30D transmitted through the second lens 12 in the positive z-axis direction.

  The protective glass 13 is a flat glass for dust prevention provided at the opening of the housing 15 in order to emit the laser beams 30C and 30D deflected by the folding mirrors 22 and 23 to the outside of the optical scanning device 1. .

  Although not particularly illustrated, the optical scanning device 1 is provided with a synchronization detection unit for acquiring a synchronization signal of the writing position of the laser beams 30A to 30D. The configuration and arrangement of the synchronization detection means are not particularly limited, and a known configuration and arrangement can be appropriately adopted as necessary. In addition, appropriate control means for performing rotational drive control of the polygon motor 9 and lighting control of the LDs 2A to D2 are provided.

Next, a schematic configuration of the image forming apparatus 50 will be described.
As shown in FIG. 1, the image forming apparatus 50 is arranged above the optical scanning apparatus 1 (on the positive side of the ζ axis), and is subjected to main scanning on a line substantially parallel to the ξ axis by the optical scanning apparatus 1. The laser beam 30A to 30D is an electrophotographic tandem apparatus that is used for exposure.
That is, the axial direction is parallel to the transfer conveyance belt 52 for conveying transfer paper (not shown), which is driven by the drive roller 53 in the left-right direction in the figure and is given tension by the tension roller 54, with a predetermined interval. The photosensitive drums 51A, 51B, 51C and 51D are arranged. The image surfaces of the laser beams 30A to 30D are set on the surfaces of the photosensitive drums 51A to 51D that are the scanned surfaces.
Although not shown in the drawing, in the circumferential direction of each photosensitive drum, a charger for uniformly charging the photosensitive drum, and charged toner are attached in accordance with the potential of the electrostatic latent image formed after exposure. A developer that visualizes the electrostatic latent image, a transfer device that transfers the visualized toner image onto the transfer paper conveyed by the transfer conveying belt 52, a cleaner that removes residual toner to reuse the photosensitive drum, and the like. Known components relating to electrophotography are arranged in this order.
For example, developing devices including toners of yellow, magenta, cyan, and black are arranged corresponding to the photosensitive drums 51A to 51D, respectively. The development method is not particularly limited, and for example, a reversal development method in which an exposed portion is developed can be employed.
Although not particularly shown, a paper feeding unit for feeding the transfer paper and a fixing device for thermally fixing the toner image transferred to the transfer paper on the transfer paper are provided upstream and downstream of the transfer conveyance belt 52.

Next, the operation of the image forming system 200 will be described focusing on the operation of the scanning optical system of the present embodiment. Since the operation of the image forming apparatus 50 is well known, detailed description thereof is omitted.
FIGS. 5A and 5B are schematic views showing the light beam transmission position in the second lens optical system for explaining the operation of the scanning optical system according to the embodiment of the present invention. FIG. 6 is a graph showing an example of scanning line bending of the scanning optical system according to the embodiment of the present invention. The horizontal axis represents the scanning angle (unit: degrees), and the vertical axis represents the amount of bending (unit: mm). FIG. 7 is a graph showing an example of the spot diameter of the image plane of the scanning optical system according to the embodiment of the present invention. The horizontal axis represents the scanning angle (unit: degree), and the vertical axis represents the spot diameter (unit: μm).

Since the operation of the scanning optical system is the same in any of the optical paths of the laser beams 30A to 30D, the following description will be given according to the positional relationship of the laser beam 30D.
First, when the LD 2D is turned on, as shown in FIGS. 3 (a) and 3 (b), the convergence is adjusted by the collimating lens 3, for example, emitted as convergent light, and orthogonal to the optical reference axis 40a by the aperture 4. A laser beam 30D having a cross-sectional shape in the direction to be emitted is emitted.
The laser beam 30D enters the cylindrical lens 6 and is condensed in the sub-scanning direction, and is slightly condensed in the main scanning direction according to the condensing action of the collimating lens 3. Then, by being reflected by the beam splitter 7, the optical reference axis 41 a is inclined by the angle θ _1, and the direction along the axial principal ray 40 a is inclined by φ _{1 in the} negative ξ axis direction with respect to the ξη plane. To the deflecting surface 8b.
On the deflection surface 8b, an image is formed in a linear shape extending in the sub-scanning direction by the action of the cylindrical lens 6, deflected at a constant angular velocity in the main scanning direction according to the rotation of the polygon mirror 8, and in the sub-scanning direction. obliquely downward according to the inclination angle phi ₁ of oblique incidence is deflected and scanned in (zeta axial negative direction in FIG. 1).

The laser beam 30D deflected by the deflecting surface 8b travels along an optical path inclined obliquely downward in the sub-scanning direction, diverges in the sub-scanning direction, and converges in the main scanning direction, while being first in the first lens 11. Incident on the surface 11a. At this time, in the oblique incidence method, the scanning line curve is generated with the rotation of the polygon mirror 8, so that the curved light beam is incident on the first lens 11 and the second lens 12.
In the present embodiment, the shape of the first surface 11a and the second surface 11b is formed by the free-form surface of the formula (1). Therefore, by changing the refractive power according to the incident position of the laser beam 30D, the second lens 12 Is incident on the first surface 12a so as to draw a scanning locus across a lens center line 42 (see FIG. 5) passing through the center reference position of the lens surface and extending in the main scanning direction.
For example, when the scanning position of the light beam toward the positive maximum image height, the image height 0, and the negative maximum image height in the effective scanning area is shown, the first surface 12a has spots 45a, 45b, 45c, FIG. On the second surface 12b, spots 46a, 46b and 46c in FIG. 5B are formed. Spot 45b is transmitted through the region of _{h 1} from the lens center line 42 in the x-axis positive direction, the spot 45a, 45 c is transmitted through the region of the maximum _{h 2} from the lens center line 42 in the x-axis negative direction.
Similarly, spot 46b is transmitted through the region of _{h 3} from the lens center line 42 in the x-axis positive direction, the spot 46a, 46c is transmitted through the region of the maximum _{h 4} from the lens center line 42 in the x-axis negative direction To do.
Then, under the light condensing action of the second lens 12, the light passes through the protective glass 13 and forms an image on the scanned surface 14.

As described above, the laser light 30D transmitted through the second lens 12 draws a scanning locus that crosses the lens center line 42 in the sub-scanning direction on the second lens 12, so that the entire locus is close to the lens center and the sub-scanning direction. The effective area at can be reduced. Here, it is preferable that h ₁ and h ₂ and h ₃ and h ₄ have substantially the same dimensions. Thereby, the effective range can be narrowed.
For example, in the conditions of the numerical examples described later, h ₁ = h ₂ = 1.5 mm, h ₃ = 1.6 mm, and h ₄ = 1.4 mm are set. In spite of the oblique incidence method, as shown in FIG. 6, it is possible to achieve a very good performance such that the scanning line bending amount is ± 0.001 mm or less.
Further, as indicated by curves 301 and 302 in FIG. 7, the image plane spot diameter in the main scanning direction and the image plane spot diameter in the sub-scanning direction are about 63 μm to 66 μm, for example, over each image height (scanning angle). An image can be formed with little variation.

On the other hand, in the numerical calculation example of the comparative example using the conditions of the prior art described later, as shown in FIG. 9, h ₁₀ , h ₂₀ , h ₃₀ , respectively corresponding to h ₁ , h ₂ , h ₃ , h ₄ , h _{40 is, h 10 = 0.1mm, h 20} = 3.2mm, h 30 = 0.1mm, and so h 40 = 3.2 mm, and eccentrically with respect to the lens center plane 42, wide effective An area is required. Further, as shown in FIG. 10, the scanning line bending amount is also about −0.009 mm to +0.015 mm, which is larger than that of the present embodiment.
The image plane spot diameter in the main scanning direction and the image plane spot diameter in the sub-scanning direction have substantially the same performance as shown by curves 401 and 402 in FIG.

  As described above, in this embodiment, the laser beams 30A to 30D that are collected as off-axis light of the first lens 11 by being obliquely incident on the polygon mirror 8 in the sub-scanning direction are converted into absolute values X and Y of position coordinates. Since the optical system is refracted by a free-form surface including the polynomial and is incident on the second lens 12 so as to straddle the lens center line 42, the scanning line bending and the spot diameter performance are sufficiently corrected, The effective range of the second lens 12 in the sub-scanning direction, which is longer than the one lens 11 and requires advanced technology for production, can be kept small. In addition, four tandem scanning optics that can be configured with one type of lens while asymmetrical aspherical shape in the main scanning direction of the second lens 12 that is required in accordance with each of the laser beams 30A to 30D is provided. The system can be realized.

  In addition, the image forming system 200 using such an optical scanning device 1 has the same operational effects and can reduce the deviation in the sub-scanning direction when the exposure images by the laser beams 30A to 30D are superimposed. For example, when a tandem color image is formed, there is an advantage that a good image quality with little color shift can be obtained.

  In the above embodiment, the first lens optical system and the second lens optical system are each a single lens. However, if there are two or more free-form surfaces of the first lens optical system, a plurality of lenses are used. You may comprise by the lens group which becomes.

Further, the above-described equations representing the free-form surfaces of the first lens optical system and the second optical lens optical system are examples, and good aberration correction is performed as an arrangement straddling the lens center line of the second lens optical system. As long as it is a free-form surface that can be used, different-form free-form surface expressions may be adopted.
In the above description, the free-form surface equations are described as examples of polynomials of X = √ (x ² ) and Y = √ (y ² ), respectively, but as necessary, x, y, X, You may represent with the numerical formula containing the polynomial of at least any combination of Y.
That is, in the at least two free-form surfaces, the position coordinate in the sub-scanning direction with respect to the center reference position is x, and the position coordinate in the main scanning direction is y, and X = √ (x ² ), Y = √ (y ² ), It may be configured by a rotationally asymmetric aspherical surface expressed by a mathematical formula including at least one of the polynomials x, y, X, and Y.

  In the above description, as the scanning optical system, two-beam scanning in which two light beams are obliquely incident on the first lens optical system is performed on two different surfaces of the optical deflector to perform four-beam scanning. As described in the example, two or more, for example, four light beams may be obliquely incident on the first lens optical system to perform four-beam scanning. In that case, the tilt angles of at least two oblique incidences of the four beams are different, but according to the present invention, the second lens optical systems can all have a common lens configuration.

Here, a case will be described where the names of the correspondence relationship between the terminology of the above embodiment and the terminology of the claims are different.
The optical scanning device 1 is an embodiment of a scanning optical device. The beam light sources 5A to 5D are an embodiment of a light source. The polygon mirror 8 is an embodiment of an optical deflector. The first lens 11 and the second lens 12 are embodiments of the first lens optical system and the second lens optical system, respectively.

  Next, numerical examples which are examples of the scanning optical system (see FIG. 4) of the above embodiment will be described. The optical conditions of this optical system are shown below.

The coordinate system of the present embodiment is the xyz coordinate system described above. Using the coordinate system, a free-form surface composed of rotationally asymmetric aspherical surfaces of the first surface 11a (s4) and the second surface 11b (s5) of the first lens 11 is expressed by Equation (1). The rotationally asymmetric aspherical surfaces of the first surface 12a (s6) and the second surface 12b (s7) are represented by Expression (2), respectively.
The numbers of the surface s, the distance d, and the refractive index n (value in the d line) in the table below correspond to those indicated by s _i , d _i , and n _i (i is an integer of 1 or more) in FIGS. To do. A refractive index not described is n = 1. The subscripts x and y mean the x-axis direction (sub-scanning direction) and the y-axis direction (main scanning direction).
The amount of eccentricity and the inclination angle are described as H and φ ₂ in FIG. Further, as shown in FIG. 3 (b), distance _{d 5} represents the size of the optical reference axis 41a.
Further, in the following units, unless otherwise specified, the length is (mm) and the angle is (°). The value of the aspheric coefficient not described is 0.

The shape of the aperture 4 is an elliptical shape in which the major axis extends in the main scanning direction and the minor axis extends in the sub-scanning direction, and the major axis × minor axis is 5.3 mm × 1.3 mm.
The incident angle θ ₁ to the polygon mirror 8 is 60 °, the scanning angle θ ₂ is 72.8 °, the wavelengths of the LDs 2A to D are 788 nm, and the photosensitive member writing width is 304 mm.
The convergence of the light beam is set to the value described in the above embodiment.

Surface s Curvature radius (x) Curvature radius (y) Distance Refractive index Eccentricity Inclination angle
1 r _1x = 41.9 r _1y = ∞ d ₁ = 3.00 n ₁ = 1.511 0 0
2 r _2x = ∞ r _2y = ∞ d ₂ = 67.86 0 0
3 r _3x = ∞ r _3y = ∞ d ₃ = 49.68 0 0
4 Free-form surface [1] d ₄ = 10.00 n ₂ = 1.525 0 0
5 Free-form surface [2] d ₅ = 71.00 0 0
6 Aspherical surface [1] d ₆ = 10.00 n ₃ = 1.525 2.7 2
7 Aspherical surface [2] d ₇ = 17.00 0 0
8 r _8x = ∞ r _8y = ∞ d ₈ = 1.90 n ₄ = 1.511 0 0
9 r _9x = ∞ r _9y = ∞ d ₉ = 100.50 0 0
Image plane ∞ ∞

Aspherical [1] (s6)
Paraxial radius of curvature 1 / CUX = 150.54 1 / CUY = -152.63
k = 0.00
Aspheric coefficient (y> 0)
A ₃ 1.48877x10 ^-4 A ₄ -2.24865x10 ^-6 A ₅ -1.19869x10 ^-9
A ₆ 4.01631x10 ^-10 A ₇ -4.11297x10 ^-12 A ₈ 1.39095x10 ^-14
Aspheric coefficient (y ≦ 0)
A ₃ 1.22529x10 ^-4 A ₄ -1.46136x10 ^-6 A ₅ -4.23228x10 ^-9
A ₆ 2.63752x10 ^-10 A ₇ -2.27234x10 ^-12 A ₈ 7.14276x10 ^-15
Aspherical [2] (s7)
Paraxial radius of curvature 1 / CUX = -42.33 1 / CUY = -275.38
k = 0.00
Aspheric coefficient (y> 0)
A ₃ 1.33436x10 ^-4 A ₄ -2.17572x10 ^-6 A ₅ -6.45045x10 ^-9
A ₆ 4.85544x10 ^-10 A ₇ -4.81268x10 ^-12 A ₈ 1.63420x10 ^-14
B ₃ 6.23116x10 ^-7 B ₄ -4.55498x10 ^-8 B ₅ 7.40463x10 ^-10
B ₆ -3.80739x10 ^-12
Aspheric coefficient (y ≦ 0)
A ₃ 1.04392x10 ^-4 A ₄ -1.39194x10 ^-6 A ₅ -1.04078x10 ^-8
A ₆ 4.00591x10 ^-10 A ₇ -3.69756x10 ^-12 A ₈ 1.26912x10 ^-14
B ₃ 1.19352
x10 ^-6 B ₄ -6.43712x10 ^-8 B ₅ 9.73294x10 ^-10
B ₆ -4.84314x10 ^-12

  According to the above optical conditions, as described in the above embodiment, the scanning line curve and the image surface spot diameter are as shown in FIGS.

Next, as a comparative example, a numerical calculation example of a scanning optical system according to the prior art is shown.
FIG. 8 is a ray diagram in the main scanning direction in a comparative example of the scanning optical system according to the related art. FIGS. 9A and 9B are schematic views showing the transmission position of the light beam in the second lens optical system of the comparative example of the scanning optical system according to the prior art. FIG. 10 is a graph showing scanning line bending in a comparative example of a scanning optical system according to the related art. The horizontal axis represents the scanning angle (unit: degrees), and the vertical axis represents the amount of bending (unit: mm). FIG. 11 is a graph showing the spot diameter of the image plane of the comparative example of the scanning optical system according to the prior art. The horizontal axis represents the scanning angle (unit: degree), and the vertical axis represents the spot diameter (unit: μm).

In the scanning optical system of the comparative example, the cylindrical lens 60, the first lens 110, the second lens 120, and the protective glass are used instead of the cylindrical lens 6, the first lens 11, the second lens 12, and the protective glass 13, respectively. 130. The first lens 110 and the second lens 120 constitute a scanning lens system 100.
The first surface s4 and the second surface s5 of the first lens 110, and the first surface s6 and the second surface s7 of the second lens 12, respectively, are aspheric surfaces represented by Expression (2).
The optical conditions of this comparative example are shown below. In addition, the positional relationship of each surface s is the same as the positional relationship of FIG. 3 (a), (b). Unless otherwise specified, the meanings and units of each table are the same as in the above examples.

The shape of the aperture 4, the incident angles θ <b> 1 and 60 degrees to the polygon mirror 8, the wavelengths of the LD <b> 2 </ b> A to D, and the photosensitive member writing width are the same as those in the above embodiment. However, the scanning angle θ2 is 76 °.
As in the above numerical example, the convergence of the light beam is converged light, and assuming that there is no subsequent optical system, the distance from the first surface s1 of the cylindrical lens 60 to the convergence position is 41 5 . 6 mm.

Surface s Curvature radius (x) Curvature radius (y) Distance Refractive index Eccentricity Inclination angle
1 r _1x = 42.5 r _1y = ∞ d ₁ = 3.00 n ₁ = 1.511 0 0
2 r _2x = ∞ r _2y = ∞ d ₂ = 67.98 0 0
3 r _3x = ∞ r _3y = ∞ d ₃ = 49.68 0 0
4 Aspherical surface [1] d ₄ = 10.00 n ₂ = 1.527 0 0
5 Aspherical surface [2] d ₅ = 71.00 0 0
6 Aspherical surface [3] d ₆ = 10.00 n ₃ = 1.527 1.8 1
7 Aspherical surface [4] d ₇ = 17.00 0 0
8 r _8x = ∞ r _8y = ∞ d ₈ = 3.00 n ₄ = 1.511 0 14
9 r _9x = ∞ r _9y = ∞ d ₉ = 89.50 0 0
Image plane ∞ ∞

Aspherical [1] (s4)
Paraxial radius of curvature 1 / CUX = 164.26 1 / CUY = -140.13
k = 0.00
Aspheric coefficient (y> 0)
A ₃ 4.73755x10 ^-5 A ₄ -2.40200x10 ^-7 A ₅ 4.66318x10 ^-8
A ₆ -5.21870x10 ^-10 A ₇ -4.05845x10 ^-13 A ₈ 6.01082x10 ^-15
Aspheric coefficient (y ≦ 0)
A ₃ 1.37707x10 ^-5 A ₄ 7.78383x10 ^-7 A ₅ 1.41738x10 ^-8
A ₆ -3.61476x10 ^-10 A ₇ -2.07187x10 ^-13 A ₈ 1.36999x10 ^-14
Aspherical [2] (s5)
Paraxial radius of curvature 1 / CUX = -738.40 1 / CUY = -83.46
k = 0.00
Aspheric coefficient (y> 0)
A ₃ 5.27362x10 ^-5 A ₄ -4.40245x10 ^-8 A ₅ 4.11717x10 ^-8
A ₆ -2.43258x10 ^-10 A ₇ -1.80503x10 ^-12 A ₈ -4.44786x10 ^-15
Aspheric coefficient (y ≦ 0)
A ₃ 2.05332x10 ^-5 A ₄ 9.74466x10 ^-7 A ₅ 1.26069x10 ^-8
A ₆ 9.74466x10 ^-7 A ₇ 8.75623x10 ^-13 A ₈ -1.86863x10 ^-14

Aspherical [3] (s6)
Paraxial radius of curvature 1 / CUX = 63.08 1 / CUY = -166.24
k = 0.00
Aspheric coefficient (y> 0)
A ₃ 9.88676x10 ^-5 A ₄ -8.25880x10 ^-7 A ₅ -3.27257x10 ^-9
A ₆ 2.47857x10 ^-11 A ₇ 7.15600x10 ^-13 A ₈ -2.30731x10 ^-15
A ₉ -1.16031x10 ^-17 A ₁₀ -1.30269x10 ^-19
Aspheric coefficient (y ≦ 0)
A ₃ 5.86214x10 ^-5 A ₄ 7.04998x10 ^-7 A ₅ -1.56633x10 ^-8
A ₆ -4.25811x10 ^-11 A ₇ 5.75476x10 ^-13 A ₈ 1.36618x10 ^-14
A ₉ -1.55905x10 ^-17 A ₁₀ -7.82859x10 ^-19
Aspherical [4] (s7)
Paraxial radius of curvature 1 / CUX = -66.56 1 / CUY = -294.76
k = 0.00
Aspheric coefficient (y> 0)
A ₃ 8.23503x10 ^-5 A ₄ -4.88945x10 ^-7 A ₅ -2.09299x10 ^-8
A ₆ 3.79620x10 ^-10 A ₇ -2.08587x10 ^-12 A ₈ -1.05333x10 ^-14
A ₉ 2.38604x10 ^-16 A ₁₀ -1.14234x10 ^-18
B ₃ -2.67291x10 ^-6 B ₄ -1.34418x10 ^-7 B ₅ 6.40862x10 ^-9
B ₆ -7.44915x10 ^-11 B ₈ 3.60934x10 ^-15 B ₁₀ -1.00153x10 ^-19
Aspheric coefficient (y ≦ 0)
A ₃ 5.36763x10 ^-5 A ₄ 1.22824x10 ^-7 A ₅ -7.64750x10 ^-9
A ₆ 2.29306x10 ^-12 A ₇ -1.17409x10 ^-12 A ₈ 2.0 1992x10 ^-14
A ₉ 4.33428x10 ^-17 A ₁₀ -1.06020x10 ^-18
B ₃ -3.18931x10 ^-6 B ₄ -1.83997x10 ^-8 B ₅ 2.00116x10 ^-11
B ₆ 6.72583x10 ^-11 B ₇ -1.25 700x10 ^-12 B ₈ 4.20945x10 ^-15
B ₉ 5.01618x10 ^-17 B ₁₀ -2.92028x10 ^-19

  According to the optical conditions of the above comparative example, as described in the above embodiment, the scanning line is bent and the image plane spot diameter is as shown in FIGS.

1 is a cross-sectional view along a sheet passing direction schematically showing a schematic configuration of a scanning optical apparatus and an image forming system according to an embodiment of the present invention. It is a top view which shows typically schematic structure of the light source part of the scanning optical system which concerns on embodiment of this invention. FIG. 3 is a schematic schematic optical path diagram in the main scanning direction and the sub-scanning direction for explaining the configuration of the scanning optical system according to the embodiment of the present invention. It is a light ray figure of the main scanning direction of the scanning optical system concerning the embodiment of the present invention. It is a schematic diagram showing the transmission position of the light beam in the 2nd lens optical system for demonstrating the effect | action of the scanning optical system which concerns on embodiment of this invention. It is a graph which shows an example of the scanning line curve of the scanning optical system concerning the embodiment of the present invention. It is a graph which shows an example of the spot diameter of the image surface of the scanning optical system which concerns on embodiment of this invention. It is a light ray figure of the main scanning direction in the comparative example of the scanning optical system which concerns on a prior art. It is a schematic diagram showing the transmission position of the light beam in the 2nd lens optical system of the comparative example of the scanning optical system which concerns on a prior art. It is a graph which shows the scanning line curve of the comparative example of the scanning optical system which concerns on a prior art. It is a graph which shows the spot diameter of the image surface of the comparative example of the scanning optical system which concerns on a prior art.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Optical scanning device 3 Collimating lens 4 Aperture 5A, 5B, 5C, 5D Beam light source (light source)
6 Cylindrical lens 8 Polygon mirror (optical deflector)
8a, 8b Deflection surface 10 Scanning lens system 11 First lens (first lens optical system)
11a, 12a First surface 11b, 12b Second surface 12 Second lens (second lens optical system)
14 Scanned surfaces 30A, 30B, 30C, 30D Laser light (light beam)
50 Image forming apparatuses 51A, 51B, 51C, 51D Photosensitive drum 200 Image forming system

Claims (4)

A plurality of light beams from the light source are incident on the light deflector from an oblique direction on a surface orthogonal to the rotation axis of the optical deflector and deflected, and the plurality of light beams are obliquely incident on the first lens optical system in the sub-scanning direction. A plurality of light beams incident and emitted from the first lens optical system are respectively incident on a plurality of second lens optical systems having different arrangement positions, and formed on different imaging planes to perform a plurality of beam scans. A scanning optical system to perform,
The first lens optical system has at least two free-form surfaces;
The positional relationship between the first lens optical system and the second lens optical system is as follows:
The light beam emitted from the first lens optical system draws a scanning trajectory straddling the lens center line extending in the main scanning direction through the center reference position of the lens surface on the entrance surface and the exit surface of the plurality of second lens optical systems. The positional relationship ,
The second lens optical system has a cross-sectional shape in the sub-scanning direction that is symmetric with respect to the lens optical axis .
In the at least two free-form surfaces, the position coordinate in the sub-scanning direction with respect to the center reference position is x, and the position coordinate in the main scanning direction is y, and X = √ (x ² ), Y = √ (y ² ) 2. The scanning optical system according to claim 1, wherein the scanning optical system includes a rotationally asymmetric aspherical surface expressed by a mathematical formula including at least one of x, y, X, and Y.   A scanning optical apparatus that performs a plurality of beam scans by including the scanning optical system according to claim 1.   An image forming system for forming an image by performing a plurality of beam scans by providing the scanning optical system according to claim 1.

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